If A is an invertible matrix of order 3, then

Match List-I with List-II

Choose the correct answer from the options given below:

(A)-(II), (B)-(IV), (C)-(I), (D)-(III)

The correct answer is Option (1) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)

Given: $A$ is an invertible $3\times 3$ matrix.

(A) $|\text{adj }A|$

For $n\times n$: $|\text{adj }A| = |A|^{\,n-1}$. Here $n=3$, so $|\text{adj }A| = |A|^2$. Matches (II)

(B) $|A(\text{adj }A)|$

$A(\text{adj }A)=|A|I$, so determinant $=|A|^3$. Matches (IV)

(C) $|2A|$

$|kA|=k^n|A|$ with $n=3$, so $|2A|=2^3|A|=8|A|$. Matches (I)

(D) $|A^{-1}|$

$|A^{-1}|=\frac{1}{|A|}$. Matches (III)

The correct matching is: A–II, B–IV, C–I, D–III.